Lebesgue integration

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Related lectures (32)

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Differential Forms and Invariant Measures

Covers differential forms, invariant measures, and integration on manifolds with examples and illustrations.

Advanced analysis II: volume change and variable transformation

Covers partitioning, integrable functions, variable transformations, and volume change in R².

Polymer Swelling Behavior

Explores the swelling behavior of polymers and its influencing factors, such as crosslinking density and solvent nature.

Fourier Transform and Schwartz Space

Explores the Fourier transform, Schwartz space, and Riemann-Lebesgue lemma in quantum physics.

Advanced Analysis II: Review of Double Integrals

Covers a review of double integrals, emphasizing compact domains and linearity.

Graph Surfaces: Integration and Vector Calculus

Covers integrating functions over graph surfaces in vector calculus, emphasizing the interpretation of divergence theorem and special cases of domain between two graphs.

Templates of (Un)stable Subbundle

Explores templates of (un)stable subbundles and the approximation of temporal-distance functions in 3-dimensional Anosov flows.

Expectation of a Random Variable

Defines the expectation for random variables, emphasizing the importance of absolute values.

Integral Calculation of Functions

Explains firm pavements, Darboux sums, and the conditions for a function to be integrable.

Integral Calculus: Riemann Integration

Explores Riemann integration for functions of several variables, Darboux sums, and the criteria for integrability.